Electronic Journal of Statistics

Analysis of juggling data: Alignment, extraction, and modeling of juggling cycles

Sebastian Kurtek, Qian Xie, and Anuj Srivastava

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Abstract

In this paper we present results from alignment, extraction, and statistical analysis of juggling trajectories using an elastic functional data analysis framework. This framework, specifically adapted for analyzing cyclostationary signals using an elastic Riemannian metric, was introduced recently by Kurtek et al. [2]. It relies on a special representation of curves called the square-root velocity function to pose the alignment problem as an optimization over the re-parametrization space. The cost function for alignment is a proper metric and is used to separate phase and amplitude components of juggling cycles. We present results of segmenting juggling trials into cycles, separating phase and amplitude components of cycles, and developing principal component analysis (PCA) based statistical models for these individual components.

Article information

Source
Electron. J. Statist. Volume 8, Number 2 (2014), 1865-1873.

Dates
First available in Project Euclid: 29 October 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1414588174

Digital Object Identifier
doi:10.1214/14-EJS937G

Mathematical Reviews number (MathSciNet)
MR3273606

Zentralblatt MATH identifier
1305.62331

Keywords
Cyclostationary processes elastic functional data analysis phase-amplitude separation cycle extraction

Citation

Kurtek, Sebastian; Xie, Qian; Srivastava, Anuj. Analysis of juggling data: Alignment, extraction, and modeling of juggling cycles. Electron. J. Statist. 8 (2014), no. 2, 1865--1873. doi:10.1214/14-EJS937G. https://projecteuclid.org/euclid.ejs/1414588174.


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References

  • [1] Kurtek, S., Srivastava, A., Klassen, E., Ding, Z. (2012), Statistical modeling of curves using shapes and related features, Journal of the American Statistical Association, 107:499, 1152–1165.
  • [2] Kurtek, S., Wu, W., Christensen, G.E., Srivastava, A. (2013), Segmentation, alignment and statistical analysis of biosignals with application to disease classification, Journal of Applied Statistics, 40:7, 1270–1288.
  • [3] Ramsay, J.O., Gribble, P., Kurtek, S. (2014), Description and processing of functional data arising from juggling trajectories., Electronic Journal of Statistics, 8, 1811–1816, Special Section on Statistics of Time Warpings and Phase Variations.
  • [4] Srivastava, A., Klassen, E., Joshi, S.H., Jermyn, I.H. (2011), Shape analysis of elastic curves in Euclidean spaces, IEEE Transactions on Pattern Analysis and Machine Intelligence, 33:7, 1415–1428.
  • [5] Srivastava, A., Wu, W., Kurtek, S., Klassen, E., Marron, J.S. (2011), Registration of functional data using Fisher-Rao metric, arXiv:1103.3817v2.
  • [6] Xie, Q., Kurtek, S., Srivastava, A. (2014), Analysis of AneuRisk65 data: Elastic shape registration of curves, Electronic Journal of Statistics, 8, 1920–1929, Special Section on Statistics of Time Warpings and Phase Variations.

See also

  • Related item: Ramsay, J. O., Gribble, P., and Kurtek, S. (2014). Description and processing of functional data arising from juggling trajectories. Electron. J. Statist. 8 1811–1816.